US 7706589 B2 Abstract A method is provided for analysis of a multi-dimensional structure which includes a tubular structure from two-dimensional datasets for respective pre-determined projection directions. A pair of corresponding initial projected centre points of the tubular structure is identified in two respective initial and further two-dimensional datasets. Projected edges of the tubular structure in said initial two-dimensional datasets and in said further two-dimensional dataset near the respective projected centre points are identified. A local size of the tubular structure is derived at the three-dimensional spatial position of the centre point of the tubular structure from said projected edges and the predetermined projection directions.
Claims(8) 1. A method for analyzing a multi-dimensional structure which includes a tubular structure having local sizes, from two-dimensional x-ray image datasets for pre-determined projection directions, the method comprising using a computer to perform the steps:
identifying at least one pair of corresponding initial projected centre points of the tubular structure in two respective initial two-dimensional x-ray image datasets,
identifying at least one further projected centre point corresponding to said initial projected centre points in at least one further two-dimensional x-ray image dataset,
deriving a three-dimensional spatial position of the centre point of the tubular structure corresponding to said initial and said at least one further projected centre points,
identifying projected edges of the tubular structure locally in said initial two-dimensional x-ray image datasets and in said further two-dimensional x-ray image dataset near the respective projected centre points, wherein identifying includes identifying on the basis of local differences between (i) brightness or grey values or (ii) local gradients of brightness or grey values in the corresponding two-dimensional x-ray image datasets and
deriving a local size of the tubular structure at the three-dimensional spatial position of the centre point of the tubular structure from (i) said projected edges and (ii) the predetermined projection directions, wherein deriving the local size yields an inscribed polygon of local cross-sectional area of the tubular structure locally at the centre point at issue, edges of said inscribed polygon corresponding to said projection edges, a number of vertices of said inscribed polygon corresponding to a number of the two-dimensional x-ray image datasets.
2. The method of
identifying a first initial projected centre point in a first initial two-dimensional x-ray image dataset
computing a first epipolar line as the intersection of a projection plane of a second initial two-dimensional x-ray image dataset and the plane spanned by the projection directions of said initial two-dimensional x-ray image datasets and
identifying a second initial projected centre point in the second initial two-dimensional x-ray image dataset on the first epipolar line in the second initial two-dimensional x-ray image dataset.
3. The method of
in at least one of the two-dimensional x-ray image datasets a series of projected centre points is identified
in said at least one two-dimensional x-ray image dataset a projected centre line is derived from said series of projected centre points
said projected centre line is corrected on the basis of a distribution of data values in the at least one two-dimensional x-ray image dataset near the projected centre line.
4. The method of
5. The method of
6. The method of
7. A computer readable storage medium storing instructions executable by a computer, the instructions being operable to perform the steps:
identifying at least one pair of corresponding initial projected centre points of the tubular structure in two respective initial two-dimensional x-ray image datasets,
identifying at least one further projected centre point corresponding to said initial projected centre points in at least one further two-dimensional x-ray image dataset,
deriving deriving a three-dimensional spatial position of the centre point of the tubular structure corresponding to said initial and said at least one further projected centre points,
identifying projected edges of the tubular structure locally in said initial two-dimensional datasets and in said further two-dimensional x-ray image dataset near the respective projected centre points, wherein identifying includes identifying on the basis of local differences between (i) brightness or grey values or (ii) local gradients of brightness or grey values in the corresponding two-dimensional x-ray image datasets and
deriving a local size of the tubular structure at the three-dimensional spatial position of the centre point of the tubular structure from (i) said projected edges and (ii) the predetermined projection directions, wherein deriving the local size yields an inscribed polygon of local cross-sectional area of the tubular structure locally at the centre point at issue, edges of said inscribed polygon corresponding to said projection edges, a number of vertices of said inscribed polygon corresponding to a number of the two-dimensional x-ray image datasets.
8. A workstation comprising an x-ray examination apparatus and a computer, the computer programmed to perform the steps:
identifying at least one pair of corresponding initial projected centre points of the tubular structure in two respective initial two-dimensional x-ray image datasets,
identifying at least one further projected centre point corresponding to said initial projected centre points in at least one further two-dimensional x-ray image dataset,
deriving a three-dimensional spatial position of the centre point of the tubular structure corresponding to said initial and said at least one further projected centre points,
identifying projected edges of the tubular structure locally in said initial two-dimensional x-ray image datasets and in said further two-dimensional x-ray image dataset near the respective projected centre points, wherein identify includes identifying on the basis of local differences between (i) brightness or grey values or (ii) local gradients of brightness or grey values in the corresponding two-dimensional x-ray image datasets and
deriving a local size of the tubular structure at the three-dimensional spatial position of the centre point of the tubular structure from (i) said projected edges and (ii) the predetermined projection directions, wherein deriving the local size yields an inscribed polygon of local cross-sectional area of the tubular structure locally at the centre point at issue, edges of said inscribed polygon corresponding to said projection edges, a number of vertices of said inscribed polygon corresponding to a number of the two-dimensional x-ray image datasets.
Description The invention pertains to a method for analysis of a multi-dimensional structure which includes a tubular structure from two-dimensional datasets. Such a method for analysis is known from the paper ‘3 The known method concerns reconstruction of a three-dimensional coronary arterial tree from two-dimensional datasets in the form of a sequence of x-ray angiograms. Such angiograms are made by injecting a patient to be examined with a contrast agent and passing x-rays from an x-ray source through the patient. The known method employs acquisition of two standard x-ray angiogram cine image sequences at respective orientations or views of the x-ray source relative to the patient. A pair of these cine images relating to corresponding phases of the heart is identified. This pair of identified corresponding cine images functions as the initial two-dimensional datasets. From each of the cine images of the corresponding pair, there are constructed vessel hierarchies that are represented by mathematical hierarchical digraph. Subsequently, a transformation characterising a spatial relationship between the views of the pair of corresponding cine images is constructed. This transformation is calculated as an optimum estimate of 3D bifurcation points given the set of 2D bifurcation points in the hierarchical digraphs. The optimum estimate is obtained as the least squares errors of the 3D bifurcation points given sets of 2D bifurcation points. Notably, the known method is employed by an x-ray examination apparatus having a moveable gantry which carries the x-ray source and an image intensifier. The gantry angulations determine the orientation of the cine images. Inaccurate values for gantry angulations are recorded in the x-ray examination apparatus. The recorded values of the gantry angulations are employed as an initial estimate of the transformation that is calculated from the hierarchical bi-graphs. An object of the invention is to provide a method of analysis of an multi-dimensional structure including a tubular structure which produces more accurate results for the local sizes of the tubular structure. This object is achieved according to the invention by a method for analysis of a multi-dimensional structure which includes a tubular structure from two-dimensional datasets for respective pre-determined projection directions, the method comprising the steps of -
- identifying at least one pair of corresponding initial projected centre points of the tubular structure in two respective initial two-dimensional datasets,
- identifying at least one further projected centre point corresponding to said initial projected centre points in at least one further two-dimensional dataset,
- derive a three-dimensional spatial position of the centre point of the tubular structure corresponding to said projected centre points,
- identify projected edges of the tubular structure in said initial two-dimensional datasets and in said further two-dimensional dataset near the respective projected centre points and
- derive a local size of the tubular structure at the three-dimensional spatial position of the centre point of the tubular structure from said projected edges and the predetermined projection directions.
The invention is based on a set of two-dimensional datasets for pre-determined projection directions. Notably, these two-dimensional datasets are formed as digitised x-ray images for respective predetermined projection directions. The projection directions are pre-determined as the x-ray projection images are generated by an x-ray examination apparatus having pre-calibrated orientations of the x-ray source and x-ray detector. Such a pre-calibrated x-ray examination apparatus is described in the international application EP01/12743 (PHNL000587). According to the present invention there are identified corresponding initial projected centre points of the tubular structure in two initial two-dimensional datasets. These projected centre points are corresponding in that they pertain to the same centre point in the tubular structure in the multi-dimensional dataset. The corresponding initial projected centre points are for example identified on the basis of features in the two-dimensional dataset that are well recognised. For example, the tubular structure may relate to a part of a patient's system of bloodvessels, notably the coronary arterial vessel tree. In the two-dimensional datasets representing projections of the system of bloodvessels, the initial projected centre points can be accurately identified on the basis of anatomical information in the projection images forming the two-dimensional datasets. Notably, suitable anatomical features are bifurcation points of the branched vessel structure which are often well recognised in the two-dimensional datasets when displayed on a display screen. Subsequently, the position in three-dimensional geometric space of the centre point in the tubular structure is calculated from the pre-determined projection directions of the initial two-dimensional datasets and the location of the initial projected centre points in these initial two-dimensional datasets. To obtain accurate values for the local size of the tubular structure in at least one further projected two-dimensional dataset at least one further projected centre point is identified. This further projected centre point also corresponds to the centre point in the tubular structure that corresponds to the initial projected centre points. That is, the initial projected centre points and further centre points in one or several further two-dimensional datasets all pertain to the same centre point in the tubular structure. In the initial two-dimensional datasets and in the further two-dimensional datasets projected edges of the tubular structure are identified locally at the projected centre points in the respective two-dimensional datasets. There are various ways to identify the projected edges e.g on the basis of (i) local differences between brightness values or grey values or (ii) local gradients of brightness or grey values in the two-dimensional datasets. From these projected edges and the pre-determined projection directions of the respective two-dimensional datasets an accurate estimate is computed of notably the cross-sectional size of the tubular structure. In particular the projected edges in the respective two-dimensional datasets and their pre-determined projection direction yield an inscribed polygon of the local cross-sectional area of the tubular structure locally at the centre point at issue. Consequently, the more two-dimensional datasets for different projection directions are employed, the larger the number of vertices of the inscribed polygon and the more accurate the estimate of the local cross section of the tubular structure on the basis of the inscribed polygon. These and other aspects of the invention will be further elaborated with reference to the embodiments defined in the dependent Claims. Preferably on the basis of the projection directions of the initial two-dimensional datasets and the spatial position of the centre point the first epipolar line is computed as the intersection of the projection plane of the second initial two-dimensional dataset and the plane spanned by the projection directions of the initial two-dimensional dataset and containing the centre point at issue in the tubular structure. The initial projected centre point in the second initial two-dimensional dataset is easily identified on the epipolar line, since only positions on the epipolar line need be considered. Moreover, the position of the projected centre point on the epipolar line is obtained very accurately. The accuracy of the position of the projected centre point in the second initial two-dimensional dataset is determined by the accuracy of the calibration of the pre-determined projection directions. It appears that the pre-determined projection directions can be calibrated at such accuracy that the position of the projected centre point is determined far more accurately than the pixel-size in the two-dimensional dataset. It is noted that further epipolar lines can be computed for any further pair of two-dimensional dataset for respective projection directions. Projected centre points are located on such epipolar lines so that identification is easily done since only positions on the epipolar line need be considered. Projected centre points can also be identified as intersections of epipolar lines pertaining to respective pairs of projection directions. In a further preferred implementation of the method according to the invention, projected centre lines of the projections of the tubular structure are constructed. These projected centre lines represent the projections of the local longitudinal axes of the tubular structure. For example the projected centre lines represent the central axis along the lumen of the blood vessel at issue as projected in the x-ray projection image. The projected centre lines are obtained from respective series of projected centre points in the individual two-dimensional datasets. Such series of projected centre points can be obtained in the same way as discussed above for the corresponding initial projected centre point and further projected centre points. The projected centre lines are for example found by connecting subsequent projected centre points in the individual two-dimensional datasets. In individual two-dimensional datasets the projected centre lines are corrected on the basis of the datavalues in the two-dimensional dataset at issue. For example the correction of the projected centre lines may be carried-out on the basis of a distribution of datavalues near the projected centre lines, on the basis of local gradients of the datavalues, local differences between datavalues or on the local Hessian matrix (i.e. local spatial 2 In particular the local size of the tubular structure is calculated as the local diameter at the centre point at issue and transversely to the corrected projected centre line. In this way the local size of the tubular structure is calculated in the respective projection directions. In this way complicated shapes, different from a circular form, of the cross section of the tubular structure is taken into account. Accurate results for in particular the projected centre line(s) are found when the initial two-dimensional datasets have projection directions that enclose an angle in the range of 30° to 150°. Very accurate results are found when the projection directions of the initial two-dimensional datasets differ about 90°. Preferably, the projection directions of the further two-dimensional datasets enclose an angle also within the range between 30° to 150°. Consequently, the range of projection directions for which the two-dimensional dataset need to be acquired is less than the full range of 180° so that accordingly the time to acquire the two-dimensional datasets is reduced. Further, it appears that the angle enclosed between the projection directions of the initial two-dimensional datasets may be selected anywhere in the range of 30° to 150°, an in particular cumbersome setting said angle at 90° is not necessary. However, it is noted for projections that differ about 90°, overlap and foreshortening of the projected tubular structure are relatively less so that corresponding centre points are easily identified. Preferably, in particular when (almost) periodic motion occurs in the tubular structure time gated acquisition of the two-dimensional dataset is employed. In time gated acquisition the datavalues of the respective two-dimensional datasets are acquired in successive time periods in which the state of motion of the tubular structure is essentially the same. For example successive two-dimensional datasets at respective projection directions at periodic instants in time at which essentially the same motion state recurs. Consequently, the two-dimensional datasets form in effect a stroboscopic representation of the tubular structure at respective projection directions. For example when the tubular structure pertains to the system of bloodvessels of the patient's heart, time gated acquisition can be carried out by ECG-triggered acquisition. The method of the invention, in particular when applied to the bloodvessel system of the patient to be examined leads to an adequate spatial rendition of the bloodvessel structure which is a useful technical tool for the physician to examine the patient's bloodvessel system. The invention further relates to a computer programme as defined in Claim These and other aspects of the invention will be elucidated with reference to the embodiments described hereinafter and with reference to the accompanying drawing wherein The object to be examined, such as a patient to be radiologically examined is placed on the patient table The two-dimensional datasets are produced in the form of x-ray projection images, which are formed on the input face of the x-ray detector At least one further two-dimensional dataset in the form of an x-ray image Patent Citations
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